Statistical Sciences

This course, intended for students considering a program in Statistical Sciences, discusses the crucial role played by statistical reasoning in solving challenging problems from natural science, social science, technology, health care, and public policy, using a combination of logical thinking, mathematics, computer simulation, and oral and written discussion and analysis.

This course explores how our statistical intuitions and ways of thinking can let us down. There’s no need to be a math whiz to be a better statistical thinker. Everyone can become a more critical consumer of claims presented in media, advertisements and by politicians—especially those relevant to our own health and wealth. This course uses real-world examples and tours common and avoidable statistical traps and tricks. Restricted to first-year students. Not eligible for CR/NCR option.

This course examines the meaning and mathematics of probabilities, and how they arise in our everyday lives. Specific topics may include: the nature of coincidences, the concept of luck, games involving dice and cards, long run averages in casinos, margins of error in polls, the interpretation of medical studies, crime statistics, decision making, pseudorandomness, and Monte Carlo algorithms. Restricted to first-year students. Not eligible for CR/NCR option.

This course explores the impact Statistics has made and continues to make on everyday life through science, law, and the modern methods for information processing. Statistical principles will be illustrated using examples from real life including business, romance and health. Restricted to first-year students. Not eligible for CR/NCR option.

This course teaches non-science students the importance of quantitative reasoning to many different areas. It explores a variety of applications to such diverse subjects as economics, gambling, politics, poetry, graphics, music, medicine, demographics, sports, secret codes, and more, using only basic high school level mathematics combined with logical thinking.

An introductory course in statistical concepts and methods, emphasizing exploratory data analysis for univariate and bivariate data, sampling and experimental designs, basic probability models, estimation and tests of hypothesis in one-sample and comparative two-sample studies. A statistical computing package is used but no prior computing experience is assumed. Note: STA220H1does not count as a distribution requirement course.

Continuation of STA220H1 (or similar course), emphasizing major methods of data analysis such as analysis of variance for one factor and multiple factor designs, regression models, categorical and non-parametric methods (Note: STA221H1 does not count as a distribution requirement course).

An introduction to probability using simulation and mathematical frameworks, with emphasis on the probability needed for more advanced study in statistical practice. Topics covered include probability spaces, random variables, discrete and continuous probability distributions, probability mass, density, and distribution functions, expectation and variance, independence, conditional probability, the law of large numbers, the central limit theorem, sampling distributions. Computer simulation will be taught and used extensively for calculations and to guide the theoretical development.

An introduction to statistical inference and practice. Statistical models and parameters, estimators of parameters and their statistical properties, methods of estimation, confidence intervals, hypothesis testing, likelihood function, the linear model. Use of statistical computation for data analysis and simulation.

Introduction to the theory of probability, with emphasis on applications in computer science. The topics covered include random variables, discrete and continuous probability distributions, expectation and variance, independence, conditional probability, normal, exponential, binomial, and Poisson distributions, the central limit theorem, sampling distributions, estimation and testing, applications to the analysis of algorithms, and simulating systems such as queues (Note: STA247H1 does not count as a distribution requirement course).

A survey of statistical methodology with emphasis on data analysis and applications. The topics covered include descriptive statistics, data collection and the design of experiments, univariate and multivariate design, tests of significance and confidence intervals, power, multiple regression and the analysis of variance, and count data. Students learn to use a statistical computer package as part of the course (Note: STA248H1 does not count as a distribution requirement course).

This courses deals with the mathematical aspects of some of the topics discussed in STA220H1. Topics include discrete and continuous probability distributions, conditional probability, expectation, sampling distributions, estimation and testing, the linear model (Note: STA255H1 does not count as a distribution requirement course).

A mathematically rigorous introduction to probability, with applications chosen to introduce concepts of statistical inference. Probability and expectation, discrete and continuous random variables and vectors, distribution and density functions, the law of large numbers. The binomial, geometric, Poisson, and normal distributions. The Central Limit Theorem. (Note: STA257H1 does not count as a distribution requirement course).

A rigourous introduction to the theory of statistical inference and to statistical practice. Statistical models, parameters, and samples. Estimators for parameters, sampling distributions for estimators, and the properties of consistency, bias, and variance. The likelihood function and the maximum likelihood estimator. Hypothesis tests and confidence regions. Examples illustrating statistical theory and its limitations. Introduction to the use of a computer environment for statistical analysis. (Note: STA261H1 does not count as a distribution requirement course).

This course is restricted to students in the Data Science Specialist program. Data exploration and preparation; data visualization and presentation; and computing with data will be introduced. Professional skills, such as oral and written communication, and ethical skills for data science will be introduced. Data science workflows will be integrated throughout the course. These topics will be explored through case studies and collaboration with researchers in other fields.

Introduction to statistics and its connection to all stages of the scientific inquiry process. Issues around data collection, analysis and interpretation are emphasized to inform study design and critical assessment of published research. Statistical software is used to conduct descriptive and inferential statistics to address basic life sciences research questions.

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-opportunities-program. Not eligible for CR/NCR option.

Introduction to data analysis with a focus on regression. Initial Examination of data. Correlation. Simple and multiple regression models using least squares. Inference for regression parameters, confidence and prediction intervals. Diagnostics and remedial measures. Interactions and dummy variables. Variable selection. Least squares estimation and inference for non-linear regression.

Analysis of variance for one-and two-way layouts, logistic regression, loglinear models, longitudinal data, introduction to time series.

Design of surveys, sources of bias, randomized response surveys. Techniques of sampling; stratification, clustering, unequal probability selection. Sampling inference, estimates of population mean and variances, ratio estimation. Observational data; correlation vs. causation, missing data, sources of bias.

Experiments vs observational studies, experimental units. Designs with one source of variation. Complete randomized designs and randomized block designs. Factorial designs. Inferences for contrasts and means. Model assumptions. Crossed and nested treatment factors, random effects models. Analysis of variance and covariance. Sample size calculations.

An introduction to data visualization and the use of visual and interactive representations of data to support human cognition. This course covers visualization techniques and algorithms based on principles from graphic design, perceptual psychology, cognitive science, and human-computer interaction. Topics include: graphic design, interaction, perception and cognition, communication, and ethics. Computational tutorials involve design review, implementation, and testing of information visualizations.

Statistical methods for supervised and unsupervised learning from data: training error, test error and cross-validation; classification, regression, and logistic regression; principal components analysis; stochastic gradient descent; decision trees and random forests; k-means clustering and nearest neighbour methods. Computational tutorials will support the efficient application of these methods.

An overview of probability from a non-measure theoretic point of view. Random variables/vectors; independence, conditional expectation/probability and consequences. Various types of convergence leading to proofs of the major theorems in basic probability. An introduction to simple stochastic processes such as Poisson and branching processes.

STA355H1 provides a unifying structure for the methods taught in other courses, and will enable students to read methodological research articles or articles with a large methodological component. Topics covered include statistical models and distributions; fundamentals of inference: estimation, hypothesis testing, and significance levels; likelihood functions and likelihood-based inference; prior distributions and Bayesian inference.

Bayesian inference has become an important applied technique and is especially valued to solve complex problems. This course first examines the basics of Bayesian inference. From there, this course looks at modern, computational methods and how to make inferences on complex data problems.

This course is restricted to students in the Data Science Specialist program. Students will learn to identify and answer questions through the application of exploratory data analysis, data visualization, statistical methods or machine learning algorithms to complex data. Software development for data science and reproducible workflows. Communication of statistical information at various technical levels, ethical practice of data analysis and software development, and teamwork skills. Topics will be explored through case studies and collaboration with researchers in other fields.

An instructor-supervised group project in an off-campus setting. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-excursions-program. Not eligible for CR/NCR option.

An instructor-supervised group project in an off-campus setting. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-excursions-program. Not eligible for CR/NCR option.

Credit course for supervised participation in faculty research project. Details at https://www.artsci.utoronto.ca/current/academics/research-opportunities/research-opportunities-program. Not eligible for CR/NCR option.

Programming in an interactive statistical environment. Generating random variates and evaluating statistical methods by simulation. Algorithms for linear models, maximum likelihood estimation, and Bayesian inference. Statistical algorithms such as the Kalman filter and the EM algorithm. Graphical display of data.

Probabilistic foundations of supervised and unsupervised learning methods such as naive Bayes, mixture models, and logistic regression. Gradient-based fitting of composite models including neural nets. Exact inference, stochastic variational inference, and Marko chain Monte Carlo. Variational autoencoders and generative adversarial networks.

This course examines current theory of statistical inference, particularly likehood-based methods and Bayesian methods with an emphasis on resolving present conflicts; log-model expansion and asymptotics are primary tools.

Practical techniques for the analysis of multivariate data; fundamental methods of data reduction with an introduction to underlying distribution theory; basic estimation and hypothesis testing for multivariate means and variances; regression coefficients; principal components and partial, multiple and canonical correlations; multivariate analysis of variance; profile analysis and curve fitting for repeated measurements; classification and the linear discriminant function.

Advanced topics in statistics and data analysis with emphasis on applications. Diagnostics and residuals in linear models, introduction to generalized linear models, graphical methods, additional topics such as random effects models, designed experiments, model selection, analysis of censored data, introduced as needed in the context of case studies.

Discrete and continuous time processes with an emphasis on Markov, Gaussian and renewal processes. Martingales and further limit theorems. A variety of applications taken from some of the following areas are discussed in the context of stochastic modeling: Information Theory, Quantum Mechanics, Statistical Analyses of Stochastic Processes, Population Growth Models, Reliability, Queuing Models, Stochastic Calculus, Simulation (Monte Carlo Methods).

Topics of current research interest are covered. Topics change from year to year, and students should consult the department for information on material presented in a given year.

Statistical theory and its applications at an advanced mathematical level. Topics include probability and distribution theory as it specifically pertains to the statistical analysis of data. Linear models and the geometry of data, least squares and the connection to conditional expectation. The basic concept of inference and the likelihood function.

Continuation of STA452H1: statistical theory and its applications at an advanced mathematical level. Topics include classical estimation, theory with methods based on the likelihood function and the likelihood statistics. Testing hypothesis and the evaluation of conference from both a bayesian and frequentist point of view.

An overview of methods and problems in the analysis of time series data. Topics include: descriptive methods, filtering and smoothing time series, theory of stationary processes, identification and estimation of time series models, forecasting, seasonal adjustment, spectral estimation, bivariate time series models.

Data acquisition trends in the environmental, physical and health sciences are increasingly spatial in character and novel in the sense that modern sophisticated methods are required for analysis. This course will cover different types of random spatial processes and how to incorporate them into mixed effects models for Normal and non-Normal data. Students will be trained in a variety of advanced techniques for analyzing complex spatial data and, upon completion, will be able to undertake a variety of analyses on spatially dependent data, understand which methods are appropriate for various research questions, and interpret and convey results in the light of the original questions posed.

This course is restricted to students in the Data Science Specialist program. Research topics and applications of data science methods will be explored through case studies and collaboration with researchers in other fields. Data analysis, visualization, and communication of statistical information at various technical levels, ethical practice of data analysis and software development, and teamwork skills.

An overview of theory and methods in the analysis of survival data. Topics include survival distributions and their applications, parametric and non-parametric methods, proportional hazards regression, and extensions to competing risks and multistate modelling.

Statistical analysis of genetic data is an important emerging research area with direct impact on population health. This course provides an introduction to the concepts and fundamentals of statistical genetics, including current research directions.  The course includes lectures and hands-on experience with R programming and state-of-the-art statistical genetics software packages.

Through case studies and collaboration with researchers in other disciplines, students develop skills in the collaborative practice of Statistics. Focus is on pragmatic solutions to practical issues including study design, dealing with common complications in data analysis, and ethical practice, with particular emphasis on written communication.

This course is intended for students completing the Statistical Science: Theory and Methods Specialist program. Novel influential ideas and current research topics in statistics will be explored through readings and discussion. Content will generally vary from semester to semester. Student presentations and written reports will be required.

Independent study under the direction of a faculty member. Students wishing to take this course must have the permission of the Department of Statistical Sciences and of the prospective supervisor. Not eligible for CR/NCR option.

Independent study under the direction of a faculty member. Students wishing to take this course must have the permission of the Department of Statistical Sciences and of the prospective supervisor. Not eligible for CR/NCR option.

Independent study under the direction of a faculty member. Students wishing to take this course must have the permission of the Department of Statistical Sciences and of the prospective supervisor. Not eligible for CR/NCR option.

Independent study under the direction of a faculty member. Students wishing to take this course must have the permission of the Department of Statistical Sciences and of the prospective supervisor. Not eligible for CR/NCR option.